Mountain pass solutions for the coupled systems of second and fourth order elliptic equations

In this paper, by the mountain pass theorem, we give an existence theorem of nontrivial solutions for a coupled system of second and fourth order elliptic equations.     

AMS theme collection on “Mechanics of Nanomaterials”

正This themed collection on Mechanics of Nanomaterials consists of five papers, including one review article. With our ability to control and manipulate matter at atomic level developed with the invention of atomic force microscope since 1980s, novel materials with feature size ranged from a few nanometer to hundreds of nanometer     

Magnetization reversal of a single cobalt cluster using a RF field pulse

Technological improvements require the understanding of dynamical magnetization reversal processes at the nanosecond time scales. In this paper, we present the first magnetization reversal measurements performed on a single cobalt cluster (counting only a thousand of spins), using the micro-superconducting quantum interference device (SQUID) technique by applying a constant magnetic field combined with a radio-frequency (RF) field pulse. First of all, we present the different technical steps necessary to detect the magnetic reversals at low temperature (T=35 mK) of a well-defined nanoparticle prepared by low energy clusters beam deposition (LECBD). We previously showed that the three-dimensional (3D)-switching Stoner-Wohlfarth astroid represents the magnetic anisotropy of the nanoparticle. Then, an improved device coupled with a gold stripe line, allow us to reverse such macrospin, using a RF pulse. A qualitative understanding of the magnetization reversal by non-linear resonance has been obtained with the Landau-Lifschitz-Gilbert (LLG) equation.     

血液可见吸收光谱与血氧参数神经网络估算法

总血红蛋白浓度和血氧饱和度是两个基本的血氧参数。文章提出了利用内置双光纤微创探头在位测量大鼠脑组织血氧参数的新方法。首先,利用悬乳液(Intralipid)和全血配置不同总血红蛋白浓度的混合溶液,模拟生物组织模型,用光纤光谱仪测试系统测量组织模型在加氧和去氧时的实时吸收光谱,同时用血氧分析仪(OXI meter)对血氧参数定标,建立测试光谱和定标数据样本集。然后,利用人工神经网络建立血液吸收光谱与血氧参数的神经网络模型,训练后的网络模型能根据吸收光谱输出生物组织的血氧参数值,总血红蛋白浓度和血氧饱和度的平均输出误差分别为±4μmol·L-1和±5%。最后,利用神经网络模型对大鼠脑组织血氧参数进行了在位测试实验,测得脑灰质的血氧饱和度为0.60~0.70,脑白质血氧饱和度为0.45~0.55;总血红蛋白浓度在脑皮层(深度1mm)附近最高,平均110μmol·L-1,其余深度脑组织的总血红蛋白浓度为70~90μmol·L-1。这种方法对脑外科微创手术中实时在位测试脑组织血氧参数具有重要的参考意义。     

Runge–Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes

In [J. Qiu, C.-W. Shu, Runge–Kutta discontinuous Galerkin method using WENO limiters, SIAM Journal on Scientific Computing 26 (2005) 907–929], Qiu and Shu investigated using weighted essentially non-oscillatory (WENO) finite volume methodology as limiters for the Runge–Kutta discontinuous Galerkin (RKDG) methods for solving nonlinear hyperbolic conservation law systems on structured meshes. In this continuation paper, we extend the method to solve two-dimensional problems on unstructured meshes, with the goal of obtaining a robust and high order limiting procedure to simultaneously obtain uniform high order accuracy and sharp, nonoscillatory shock transition for RKDG methods. Numerical results are provided to illustrate the behavior of this procedure.     

Nonlinear evolution of turbulent spots in the near-wall shear flow

The initial model of turbulent spots with the wall disturbance using the pulse form was proposed. A group of three-dimensional coupling compact difference schemes with high accuracy and high resolution were developed, and implemented to simulate the formation and development of turbulent spots in the near-wall shear flow by means of direct numerical simulation of the Navier-Stokes equations. Growing and decaying modes were used to analyze nonlinear evolution characteristics of the turbulent spots.     

Electron paramagnetic resonance studies on manganite Pr0.5Sr0.5Mn1−x Ga x O3 (x=0 and 0.05)

In this paper, we present the investigations of electron paramagnetic resonance on perovskite manganite Pr_0.5Sr_0.5MnO₃ and Ga-doped Pr_0.5Sr_0.5Mn_0.95Ga_0.05O₃. The temperature dependent paramagnetic resonance spectra parameters (effective g-factor, peak-to-peak linewidth ΔH _pp and double integrated intensities) have been used to study the paramagnetic spin correlations and spin dynamics. The gradual increase of effective g-factor is attributed to the presence of orbital ordering above T _C. The model fittings of temperature dependent double integrated intensities reveal Arrhenius law is appropriate for describing Pr_0.5Sr_0.5Mn_0.95Ga_0.05O₃ instead of Pr_0.5Sr_0.5MnO₃ system. As for Pr_0.5Sr_0.5MnO₃, the broadening of linewidth with the temperature increase origins from the contribution of small polaron hopping in the PM regime. However, as for Pr_0.5Sr_0.5Mn_0.95Ga_0.05O₃, the broadening of EPR linewidth can be understood with the spin-lattice relaxation mechanism.     

Radiation-induced changes in electrical conductivity and structure of BaPbO3 after γ-irradiation

Several barium plumbate (BaPbO₃) solid samples, made from PbO and BaCO₃ powder by chemistry liquid-phase coprecipitation, were investigated before and after γ-irradiation. The solid samples were irradiated by a ⁶⁰Co γ-irradiation source whose dose rate is about 0.7?kGy per hour. The irradiation times were 0, 72, 144, 216, 288 and 360?h. Then, the four-probe method, X-ray diffraction (XRD), scanning electron microscope (SEM) and X-ray photoelectron spectroscopy (XPS) were used to indicate the changes in electrical conductivity and microstructure of BaPbO₃ after γ-irradiation. The XRD results indicated that the content of PbO was reduced as the irradiation dose was increased and eventually vanished from the surface of samples. However, there was no new obvious substance phase found from the XRD atlas. It seems that the PbO transformed into nearly amorphous Pb₅O₈. The conjecture could be proved by the results of annealing experiment and SEM. The XPS results seem to show that the microstructure of BaPbO₃ was slightly changed.     

Quantum Pattern Recognition with Probability of 100%

In recent years there has been an increasing focus on the quantum pattern recognition, especially quantum multi-pattern recognition in computer science. This paper presents a new quantum multi-pattern recognition method based on the improved Grover’s algorithm. This method not only details the process of quantum multi-pattern recognition using several unitary operators, but also introduces a new design scheme of initializing quantum state and quantum encoding on the pattern set. If the rate of the number of the recognized pattern on the total patterns is over 1/3, this new method can recognize multi-pattern simultaneously with the probability of 100%. Mathematic calculations and simulation results on the case show that the proposed method can accomplish multi-pattern recognition with the probability of 100%. However, the recognition probability of other pattern recognition methods is impossible to reach 1.